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arXiv · 2007.05388

Minimal velocity bound for Schroedinger-type operator with fractional powers

Atsuhide Ishida
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Abstract

It is known in scattering theory that the minimal velocity bound plays a conclusive role in proving the asymptotic completeness of the wave operators. In this study, we prove the minimal velocity bound and other important estimates for the two-body Schroedinger-type operator with fractional powers. We assume that the pairwise potential functions belong to broad classes that include long-range decay and Coulomb-type local singularities. Our estimates are expected to be applied to prove the asymptotic completeness for the fractional Schroedinger-type operators in various (not only short-range but also long-range and N-body) situations.

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Atsuhide Ishida. 2020-07-10. Minimal velocity bound for Schroedinger-type operator with fractional powers. https://arxiv.org/abs/2007.05388

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